Calculate the final temperature (once the ice has melted) of a mixture made up initially of 75.0 ml liquid water at 29.0 degrees C and 7.0 g ice at 0.0 degrees C.
q1 = heat to melt ice at zero C.
q1 = mass ice x heat fusion.
q2 = heat to move temperature liquid water (from the ice) at zero C to final T.
q2 = mass water x specific heat water from ice x (Tfinal-Tinitial).
q3 = heat to move 75 mL water from 29 to tinal T.
q3 = mass 75 mL water x specific heat water x (Tfinal-Tinitial).
Total Q = q1 + q2 + q3.
Watch the signs and watch the units.
q1 = +6.3 µC q2 = +2.6 µC q3 = −3.9 µC = 0 cm, x = 2.0 cm x = 5.5 cm
To calculate the final temperature of the mixture once the ice has melted, we need to take into account the heat gained by the ice as it melts and the heat lost by the water as it cools down.
Here's how to calculate it step by step:
1. Calculate the heat gained by the ice:
The heat gained by the ice can be calculated using the formula: Q = m * ΔHf, where Q is the heat gained, m is the mass of the ice, and ΔHf is the heat of fusion (amount of heat needed to melt one gram of ice at 0 degrees C). The heat of fusion of water is approximately 334 J/g.
Q_ice = (7.0 g) * (334 J/g) = 2338 J
2. Calculate the heat lost by the water:
The heat lost by the water can be calculated using the formula: Q = m * c * ΔT, where Q is the heat lost, m is the mass of the water, c is the specific heat capacity of water (approximately 4.18 J/g°C), and ΔT is the change in temperature (final temperature - initial temperature).
Given:
Initial temperature of water (T1) = 29.0°C
Specific heat capacity of water (c) = 4.18 J/g°C
Volume of water (V) = 75.0 ml = 75.0 g (since the density of water is approximately 1 g/ml)
Using the formula Q = m * c * ΔT, we can rearrange it to find ΔT:
Q_water = -Q_ice (since the heat gained by the ice is equal to the heat lost by the water, but with opposite sign)
(75.0 g) * (4.18 J/g°C) * (ΔT) = -2338 J
Solving for ΔT:
ΔT ≈ -7.1°C
However, we need to keep in mind that the final temperature (once the ice has melted) should be positive, so we can disregard the negative sign. Therefore, the change in temperature is approximately 7.1°C.
3. Calculate the final temperature of the mixture:
To find the final temperature, we can add the initial temperature of the water (T1) to the change in temperature (ΔT):
Final temperature = Initial temperature + ΔT
Final temperature = 29.0°C + 7.1°C
Final temperature ≈ 36.1°C
Therefore, the final temperature of the mixture once the ice has melted is approximately 36.1°C.